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Abstract A truly three-dimensional (3D) gas-kinetic flux solver for simulation of incompressible and compressible viscous flows is presented in this work. By local reconstruction of continuous Boltzmann equation, the inviscid and viscous fluxes across the cell interface are evaluated simultaneously in the solver. Different from conventional gas-kinetic scheme, in the present work, the distribution function at cell interface is computed in a straightforward way. As an extension of our previous work (Sun et al., Journal of Computational Physics, 300 (2015) 492–519), the non-equilibrium distribution function is calculated by the difference of equilibrium distribution functions between the cell interface and its surrounding points. As a result, the distribution function at cell interface can be simply calculated and the formulations for computing the conservative flow variables and fluxes can be given explicitly. To validate the proposed flux solver, several incompressible and compressible viscous flows are simulated. Numerical results show that the current scheme can provide accurate numerical results for three-dimensional incompressible and compressible viscous flows.

A truly three-dimensional (3D) gas-kinetic flux solver for simulation of incompressible and compressible viscous flows is presented in this work. By local reconstruction of continuous Boltzmann equation, the inviscid and viscous fluxes across the cell interface are evaluated simultaneously in the solver. Different from conventional gas-kinetic scheme, in the present work, the distribution function at cell interface is computed in a straightforward way. As an extension of our previous work (Sun et al., Journal of Computational Physics, 300 (2015) 492–519), the non-equilibrium distribution function is calculated by the difference of equilibrium distribution functions between the cell interface and its surrounding points. As a result, the distribution function at cell interface can be simply calculated and the formulations for computing the conservative flow variables and fluxes can be given explicitly. To validate the proposed flux solver, several incompressible and compressible viscous flows are simulated. Numerical results show that the current scheme can provide accurate numerical results for three-dimensional incompressible and compressible viscous flows. [ABSTRACT FROM AUTHOR]

In this work, a truly three-dimensional (3D) flux solver is presented for simulation of inviscid compressible flows. Like the conventional multi-dimensional gas-kinetic scheme, in the present work, the local solution of 3D Boltzmann equation at the cell interface is used to evaluate the flux. On the other hand, different from most of the existing gas-kinetic schemes, which are constructed from Maxwellian distribution function, the present flux solver is derived from a simple distribution function defined on the spherical surface in the phase velocity space. As a result, the explicit expression of flux vector at the cell interface can be simply given. Since the simple distribution function is defined on the spherical surface, for simplicity, it is termed as sphere function hereafter. In addition, to simulate fluid flow problems with strong shock waves, the non-equilibrium part of the distribution function is regarded as numerical dissipation and involved in evaluating the inviscid flux at the cell interface. The weight of the non-equilibrium part is controlled by introducing a switch function which ranges from 0 to 1. In the smooth region, the switch function takes a value close to zero, while around the strong shock wave, it tends to one. To validate the proposed flux solver, several transonic, supersonic and hypersonic inviscid flows are simulated. Numerical results showed that the present solver can provide accurate numerical results for three-dimensional inviscid flows with strong shock waves. [ABSTRACT FROM AUTHOR]